HRABOVE, Ukraine—They could have been local plumbers or painters. Three men dressed in civilian work clothes were putting on purple latex gloves and preparing to trudge through a field outside this separatist-held village to continue retrieving bodies from the crash of Malaysia Airlines Flight 17 on Thursday.

The men wore plain clothes and assisted uniformed regional emergency services workers. For the first time on Saturday, they started gathering whole and dismembered bodies from the rebel-controlled crash site, where...